I want to implement database mirroring, but can't afford downtime for a full backup, copy to mirror and restore....I need to know if after I switch on mirroring if the mirror will "catch up" the 3 hours worth of data that came in on the principal while I did the initial restore on the mirror?

Sorry if I sound confusing. I hope someone that has done something similar can offer some advice..

By downtime I meant must I stop all my insert adapters so that there is no activity on my principal for the time it takes me to do the restore on the mirror, and then start them again when I'm done with the restore and ready to start mirroring.

But I think it makes sense that I don't need to do that and that the data will just catch up?

Providing you've taken no log backups between the backups that got copied and the configuring of the mirror, yes it will catch up. If you have, all those log backups need to also be copied and restored on the mirror before you can start the mirroring.